The Rock–Water–Ice Topographic Gravity Field Model RWI_TOPO_2015 and Its Comparison to a Conventional Rock-Equivalent Version

Abstract

RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the $5'\times 5'$ global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the $1'\times 1'$ Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model.

Appendix

In addition to the investigations for the gravity disturbance $\delta g$ as presented in Sect. 5, this appendix provides further results in the case of the height anomaly $\zeta$ (Eq. (41)) and the gravity gradient $M_{33}$ (Eq. (43)). In Figs. 18 and 19, the topographic signal of RWI_TOPO_2015, RWI_TOPO_2015_Rock, RWI_TOPO_2015_Water, and RWI_TOPO_2015_Ice is plotted in terms of $\zeta$ and $M_{33}$, respectively, while corresponding statistics are presented in Tables 10 and 11. For the comparison of RWI_TOPO_2015 to RWI_TOPO_2012 and REQ_TOPO_2015, Figs. 20 and 21 show differences in terms of $\zeta$ and $M_{33}$, respectively. Corresponding statistics for these cases can be found in Tables 12, 13, 14 and 15.

Table 10 Statistics of the RWI_TOPO_2015 topographic signal and its rock, water, and ice proportions in terms of height anomalies $\zeta$ evaluated on the surface of the GRS80 ellipsoid

Table 11 Statistics of the RWI_TOPO_2015 topographic signal and its rock, water, and ice proportions in terms of the gravity gradient $M_{33}$ evaluated on a spherical grid at a mean GOCE satellite altitude ($254.9\,\text {km}$)

Table 12 Statistics of the difference of RWI_TOPO_2015 and RWI_TOPO_2012 in terms of height anomalies $\zeta$ evaluated on the surface of the GRS80 ellipsoid

Table 13 Statistics of the difference of the RWI_TOPO_2015 and REQ_TOPO_2015 topographic signal and their water and ice proportions in terms of height anomalies $\zeta$ evaluated on the surface of the GRS80 ellipsoid

Table 14 Statistics of the difference of RWI_TOPO_2015 and RWI_TOPO_2012 in terms of the gravity gradient $M_{33}$ evaluated on a spherical grid at a mean GOCE satellite altitude ($254.9\,\text {km}$)

Table 15 Statistics of the difference of the RWI_TOPO_2015 and REQ_TOPO_2015 topographic signal and their water and ice proportions in terms of the gravity gradient $M_{33}$ evaluated on a spherical grid at a mean GOCE satellite altitude ($254.9\,\text {km}$)

Fig. 18

Topographic signal of a RWI_TOPO_2015, b RWI_TOPO_2015_Rock, c RWI_TOPO_2015_Water, and d RWI_TOPO_2015_Ice in terms of height anomalies $\zeta$ evaluated on the surface of the GRS80 ellipsoid. Robinson projection centered at $0^\circ$ longitude

Fig. 19

Topographic signal of a RWI_TOPO_2015, b RWI_TOPO_2015_Rock, c RWI_TOPO_2015_Water, and d RWI_TOPO_2015_Ice in terms of the gravity gradient $M_{33}$ evaluated on a spherical grid at a mean GOCE satellite altitude ($254.9\,\text {km}$). Robinson projection centered at $0^\circ$ longitude

Fig. 20

Difference of RWI_TOPO_2015 to a RWI_TOPO_2012 and b REQ_TOPO_2015 in terms of height anomalies $\zeta$ evaluated on the surface of the GRS80 ellipsoid. Robinson projection centered at $0^\circ$ longitude

Fig. 21

Difference of RWI_TOPO_2015 to a RWI_TOPO_2012 and b REQ_TOPO_2015 in terms of the gravity gradient $M_{33}$ evaluated on a spherical grid at a mean GOCE satellite altitude ($254.9\,\text {km}$). Robinson projection centered at $0^\circ$ longitude